Since you said you're going for a math PhD, my experience (I have a math PhD
and switched from Windows to linux years ago for similar reasons) might
help. In addition to latex (and kdvi, etc) and python you'll probably want to use
SAGE at some point (SAGE = Software for Algebra and Geometry Exploration, sage.scipy.org). SAGE is developed on ubuntu and Macs but works under SUSE and Redhat and probably other flavors of linux. However, it does not work well under
VMWare.
If you have trouble setting up a dual boot for some reason, you might also consider colinux. My understanding (I've never used it) is that colinux is essentially linux sitting in windows. I've not used it but heard from some people that it is better than cygwin in some ways. Probably if you google colinux, you find more info. Good luck!